Density

An eraser has a mass of $30\ \text{g}$ and occupies a volume of $15\ \text{cm}^3$. Calculate its density in $\text{g/cm}^3$ (remember: $d = m/V$).

A block of pine wood weighs $120\ \text{g}$ and has a volume of $200\ \text{cm}^3$. What is its density? Express the result in $\text{g/cm}^3$.

An iron nut has a mass of $79\ \text{g}$ and a volume of $10\ \text{cm}^3$.

1. a) Calculate its density.
2. b) State whether it is greater or less than the density of water, which is $1\ \text{g/cm}^3$.

In the kitchen, there is a bottle containing $500\ \text{cm}^3$ of oil. The density of oil is $0,9\ \text{g/cm}^3$. Calculate the mass of the oil (hint: rearrange for $m$ in the formula $d = m/V$).

A gold ingot has a mass of $386\ \text{g}$ and the density of gold is $19,3\ \text{g/cm}^3$. Calculate the volume of the ingot by rearranging for $V$ in the formula $d = m/V$. Express the result in $\text{cm}^3$.

To find the density of a stone, Sara first weighs it on the balance: $54\ \text{g}$. Then she pours $60\ \text{mL}$ of water into a measuring cylinder and, on submerging the stone, the level rises to $80\ \text{mL}$, as shown in the figure.

1. a) What is the volume of the stone, in $\text{cm}^3$?
2. b) Calculate its density.
3. c) The density of granite is $2,7\ \text{g/cm}^3$. Could the stone be made of granite? Reason your answer.

You have made a plasticine figure and want to calculate its density in the laboratory.

1. a) Which two quantities do you need to measure?
2. b) Which instrument do you use to measure each of them?
3. c) What calculation do you perform with the two measurements to find the density?

The density of water is $1\ \text{g/cm}^3$.

1. a) Knowing that $1\ \text{g/cm}^3 = 1000\ \text{kg/m}^3$, express the density of water in $\text{kg/m}^3$, which is the International System unit.
2. b) What is the mass of $1\ \text{m}^3$ of water?

You want to measure the density of a cork stopper using a balance and a measuring cylinder, but a problem arises: the cork floats and does not submerge on its own, so the water in the measuring cylinder does not show its full volume.

1. a) Describe a trick to measure the total volume of the stopper (for example, tying it to a heavy object that sinks). State which measurements you would make with the measuring cylinder.
2. b) The stopper weighs $4,8\ \text{g}$ and, measured using your trick, its volume turns out to be $20\ \text{cm}^3$. Calculate its density.
3. c) Check that the result explains why cork floats in water ($1\ \text{g/cm}^3$).

The density of cork is $0,24\ \text{g/cm}^3$ and that of water is $1\ \text{g/cm}^3$, as shown in the diagram.

1. a) What happens if you drop a cork stopper into a glass of water? Justify your answer by comparing their densities.
2. b) What if you drop a steel coin, whose density is $7,9\ \text{g/cm}^3$? Justify your answer in the same way.

An ice cube (density $0,92\ \text{g/cm}^3$) falls into a glass of water (density $1\ \text{g/cm}^3$), as shown in the diagram.

1. a) Does it float or sink? Justify your answer by comparing their densities.
2. b) Relate your answer to the fact that icebergs float in the sea.

A plastic ball has a mass of $150\ \text{g}$ and a volume of $200\ \text{cm}^3$.

1. a) Calculate its density.
2. b) Will it float in water, whose density is $1\ \text{g/cm}^3$? Justify your answer by comparing the densities.

In a glass, we carefully pour three liquids that do not mix with each other: honey ($1,4\ \text{g/cm}^3$), water ($1\ \text{g/cm}^3$) and oil ($0,9\ \text{g/cm}^3$), as shown in the figure.

1. a) Order the three liquids from most dense to least dense.
2. b) Predict which liquid will remain at the bottom of the glass, which in the middle and which at the top, and justify your prediction.

A sheet of steel dropped into water sinks (the density of steel is $7,9\ \text{g/cm}^3$), yet a steel ship weighing thousands of tonnes floats in the sea, as shown in the figure.

1. a) Explain the role played by the air inside the hull: what can you say about the average density of the ship (including the air) compared to that of water?
2. b) Predict what happens if an impact creates a hole in the hull and water takes the place of the air. Justify your answer using the concept of average density.

A submarine has tanks that it can fill with sea water or empty by pushing the water out, as shown in the figure.

1. a) When the submarine wants to submerge, it fills the tanks with water. Explain what happens to its average density and why this causes it to sink.
2. b) What does it do with the tanks when it wants to return to the surface? Justify your answer using average density.
3. c) Fish do something similar with the swim bladder, an organ they inflate or deflate to rise or descend in the water. Explain the similarity with the submarine.